Question

find the sine of $\angle s$.
write your answer in simplified, rationalized form. do not round.
$\sin(s) = $

Explanation:

Step1: Recall sine definition for right triangles

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle S$

Opposite side to $\angle S$ is $TU = 6$, hypotenuse is $US = \sqrt{47}$

Step3: Substitute into sine formula

$\sin(S) = \frac{6}{\sqrt{47}}$

Step4: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{47}$:
$\sin(S) = \frac{6 \times \sqrt{47}}{\sqrt{47} \times \sqrt{47}} = \frac{6\sqrt{47}}{47}$

Answer:

$\frac{6\sqrt{47}}{47}$